The effect of formal representation on the learning of ratio concepts

Abstract A study was made of the formal representation of blue and yellow color mixtures as rational numbers and its effect on students' ability to solve ratio problems comparing these mixtures. Children in grade 7, 8, and 9 were first given comparison of mixtures problems with an opportunity to watch the actual outcome and check their predictions (Task 1). They were then asked to solve similar problems, after being introduced to the representation of the mixtures as rational numbers (Task 2), and finally tested on their ability to reach a general solution to problems of the same nature (Task 3). Analysis of the various strategies employed by the students on the different tasks showed that a substantial number of students improved their performance as a result of introducing the formal representation of the problems.